Closed-form-jitter

MATLAB Code for performing the interval jitter hypothesis test in a closed-form fashion.

Abstract

Interval jitter and spike resampling methods are used to analyze the time scale on which temporal correlations occur. They allow the computation of jitter corrected cross correlograms and the performance of an associated statistically robust hypothesis test to decide whether observed correlations at a given time scale are significant. Currently used Monte Carlo methods approximate the probability distribution of coincidences. They require generating $N_{\rm MC}$ simulated spike trains of length $T$ and calculating their correlation with another spike train up to lag $\tau_{\max}$. This is computationally costly $O(N_{\rm MC} \times T \times \tau_{\max})$ and it introduces errors in estimating the $p$ value. Instead, we propose to compute the distribution in closed form, with a complexity of $O(C_{\max} \log(C_{\max}) \tau_{\max})$, where $C_{\max}$ is the maximum possible number of coincidences. All results are then exact rather than approximate, and as a consequence, the $p$-values obtained are the theoretically best possible for the available data and test statistic. In addition, simulations with realistic parameters predict a speed increase over Monte Carlo methods of two orders of magnitude for hypothesis testing, and four orders of magnitude for computing the full jitter-corrected cross correlogram.

Publication

The code here was was developed for the following technical report.

@TechReport{Jeck_Niebur15c,
  Title                    = {Closed Form Jitter Analysis of Neuronal Spike Trains},
  Author                   = {Daniel Jeck and Ernst Niebur},
  Institution              = {Zanvyl Krieger Mind/Brain Institute, Johns Hopkins University},
  Year                     = {2015},
  Note                     = {arXiv:1502.07907 [q-bio.NC]},
  Number                   = {DJEN-2015.1},

  Owner                    = {niebur},
  Timestamp                = {2015.02.27}
}

If you use this code in your own work please cite it.

This work was also presented at CISS 2015

D. Jeck and E. Niebur, "Closed form jitter methods for neuronal spike train analysis," 2015 49th Annual Conference on Information Sciences and Systems (CISS), Baltimore, MD, 2015, pp. 1-3. doi: 10.1109/CISS.2015.7086908

Files

The function to perform the interval jitter hypothesis test is jitter_closed_form.m, which calls generate_table.m.

speed_test.m and speed_test2.m were used to generate the figures in the technical report.